Solution:

For an ideal frictionless banked curve, the optimum speed is given by \(v = \sqrt{gRtan\theta}\). Given R = 90 m, \(\theta = 45^\circ\), and assuming \(g = 10\text{ m/s}^2\), \(v = \sqrt{10 \times 90 \times tan 45^\circ} = \sqrt{900 \times 1} = 30\text{ m/s}\).